The sum of the digits of a two - digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number. Check your solution.

Question

Philoid · Accepted Answer

Let the digits be x and y so the number = (10x + y), on reversing the digits number = (10y + x)

According to the question

x + y = 12 - (A)

And 10y + x - 10x - y = 54

⇒ 9y - 9x = 54

⇒ y - x = 54/9 = 6

⇒ y = 6 + x

Putting in (A) we get

x + 6 + x = 12

⇒ 2x = 6

⇒ x = 3

⇒ y = 6 + x = 9

So the number is 39

Checking the answer:

Digit sum = 3 + 9 = 12

Reversing the digits number becomes = 93

93 - 39 = 54

Hence, verified.